Solve (x+6)(x-5)-(x-3)(2-x)=(2x-1)(x+2)

$$( x + 6 ) ( x - 5 ) - ( x - 3 ) ( 2 - x ) = ( 2 x - 1 ) ( x + 2 )$$

Solve for x

$$x = -\frac{22}{7} = -3\frac{1}{7} \approx -3.142857143$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+6 by x-5 and combine like terms.

$$x^{2}+x-30-\left(x-3\right)\left(2-x\right)=\left(2x-1\right)\left(x+2\right)$$

Use the distributive property to multiply x-3 by 2-x and combine like terms.

$$x^{2}+x-30-\left(5x-x^{2}-6\right)=\left(2x-1\right)\left(x+2\right)$$

To find the opposite of 5x-x^{2}-6, find the opposite of each term.

$$x^{2}+x-30-5x+x^{2}+6=\left(2x-1\right)\left(x+2\right)$$

Combine x and -5x to get -4x.

$$x^{2}-4x-30+x^{2}+6=\left(2x-1\right)\left(x+2\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-4x-30+6=\left(2x-1\right)\left(x+2\right)$$

Add -30 and 6 to get -24.

$$2x^{2}-4x-24=\left(2x-1\right)\left(x+2\right)$$

Use the distributive property to multiply 2x-1 by x+2 and combine like terms.

$$2x^{2}-4x-24=2x^{2}+3x-2$$

Subtract 2x^{2} from both sides.

$$2x^{2}-4x-24-2x^{2}=3x-2$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-4x-24=3x-2$$

Subtract 3x from both sides.

$$-4x-24-3x=-2$$

Combine -4x and -3x to get -7x.

$$-7x-24=-2$$

Add 24 to both sides.

$$-7x=-2+24$$

Add -2 and 24 to get 22.

$$-7x=22$$

Divide both sides by -7.

$$x=\frac{22}{-7}$$

Fraction \frac{22}{-7} can be rewritten as -\frac{22}{7} by extracting the negative sign.

$$x=-\frac{22}{7}$$